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Taking advantage of gauge transformation and dipolar approximation, we qualitatively derive rotating Bose-Hubbard model.Then finite temperature phase boundary between superfluid phase and normal state in rotating Bose-Hubbard model is analytically derived by studying the stability of normal state in rotating bosonic optical lattice.We also analytically prove that as the function of rotation angular velocity the oscillation of critical hopping matrix directly follows the upper boundary of Hofstadter butterfly.

4通过做一个规范变换和偶极近似，定性地推导了旋转Bose-Hubbard模型，并且通过研究正常态不动点的稳定性推广了旋转Bose-Hubbard模型的零温相图到有限温度的情形；另外根据系统有效的能带宽度与旋转速度的关系(Hofstadter蝴蝶)，得到了系统的临界跃迁矩阵随旋转速度的改变展示谐振行为的结论。

Differing from the general BEM that is attributed from the general boundary integral equation, The natural boundary element method attributed from the natural BIE has not only the advantage of the dimensionality, but is confirmed and gain the only NBIE from the original problem.

无网格方法仅仅需要节点信息，克服了有限元等传统数值方法对网格有较强依赖性的缺点，摆脱了网格的束缚，避免了大量的网格分划、复杂的网格生成及重新划分的工作，减少了因网格畸变而引起的困难，而且收敛快、精度高、易于实现和进行后处理工作。

According to the boundary condition of the actual rectangular plates, it is very easy to get the characteristic equation for the problem through the boundary value of the generalized solution.

根据实际矩形板的边界条件，再应用弹性矩形薄板稳定问题的广义位移解的边界值，很容易便可得到该稳定问题的特征方程。

Himalaya, which formed on the basement of the Pan-African orogenic event at about 550 Ma BP and experienced Ordovician to Devonian platform sedimentation, was transformed into to a back-arc extensional-rifted zone at the end of the Carboniferous. The Yarlung Zangbo ophiolitic mélange zone is a Mesozoic back-arc spreading basin corresponding to the Gangdise paleo-island arc zone on the south side of the Tethyan Ocean. The Gangdise zone experienced island-arc orogeny in the Late Paleozoic. The very significant differences in geology on both sides of the Bangong Co-Nujiang suture zone suggest that the suture zone is not only the northern boundary of Gondwanaland and the boundary between the Indian (Yunnan-Tibet) stratigraphic realm and the South China (Qiangtang-Sanjiang) stratigraphic realm, but also the relics of subductional collision and final extinction of the Phanerozoic Tethyan Ocean after the breakup of the Neoproterozoic supercontinent Rodinia. The basic point of study of the collisional orogenic processes of the plateau is the structure and composition of the archipelagic arc-basin tectonic realm of three different stages bounded by three rigid paleocontinental blocks (Gondwanaland, Laurasia and Pan-Cathaysian) and the mutual constraining, transformation and coupling of various material movement forms.

喜马拉雅奠基于5.5亿年左右的泛非造山事件基底上，历经奥陶纪至泥盆纪台地沉积，并于石炭纪末转化为印度板块北缘的弧后伸展裂陷带；雅鲁藏布江蛇绿混杂岩带曾是特提斯大洋南侧与冈底斯古岛弧带相对应的中生代弧后扩张盆地；冈底斯带曾经历了晚古生代岛弧造山作用；班公湖-怒江带两侧大量地质特征重大差异表明，班公湖-怒江带是冈瓦纳大陆北界，是印度地层区和华南地层区的分界，是新元古代Rodinia超大陆解体后显生宙特提斯大洋俯冲，消减，碰撞，最后消亡的遗迹。

There are various complex interactive relationships between the original system and the environment system in an expending system; therefore the band boundary becomes a gradational boundary.

在全系统中，由于本体系统与环境系统之间会产生各种各样非常复杂的相互作用关系，因而本体系统的边界就成了一个具有丰富层次的环带边界。

On one hand, the grain boundaries are the sites of microcrack nucleation, microcracks first occur at grain boundary zone, whose propagation type depends on lamellar orientation of both side of grain boundary.

一方面，微裂纹首先萌发于晶界区，其扩展方式取决于晶界两侧片层的取向。

Boundary representation, involves actually drawing the boundary of the model so that it appears on the display of a graphics terminal.

界限表示法，介入实际上得出模型的界限，以便它在图形终端的显示出现。

Boundary features are the boundary lines of a group of points distributed on a fitting feature.

边界特徵之萃取理论是利用拟合特徵所给予之资讯，找出属於边界之点云资料，再由这些边界点云资料计算出边界特徵。

The total transmission ratio, the relationship between basic transmission ratio and closed transmission ratio and their influences on efficiency were studied on the H typed closed epicyclic train, and the expression of boundary region of basic transmission ratio under conditions of satisfying the allowable efficiency was gained and the boundary curve was drawn.

研究了H封闭式周转轮系总传动比、基础传动比与封闭传动比之间的关系及其对效率的影响，得到了在满足许用效率的条件下基础传动比边界区域表达式，绘出了边界曲线。

The improved e-N method can also yield results well agree with those obtained by DNS.4 The transition prediction for boundary layers on cones with different key parameters such as angle of attack, cone half angle and the Mach number of the coming flow, have been made, to show the reliability of the modified e-N method.5 For the calculation of base flow, boundary layer equations can be used in the case of small angle of attack.

但是它要依赖于对初始扰动的正确预估，这显然又取决于更多飞行数据的积累和分析。e-N方法的转捩预测结果与直接数值模拟得到的结果也吻合较好。4通过对不同来流攻角、不同半锥角和不同马赫数的三维圆锥边界层的转捩位置进行预测，证实了改进的e-N方法对于三维边界层转捩预测是可靠的。5对于基本流的计算，边界层方程可以用于小攻角的情况，其计算量远远小于直接数值模拟，但背风面的剖面不可靠。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。